dear
all,
sorry for arriving late - been busy marking (appalling) exams
and projects over the last few days.
Coming to the issue, I confess I fail to see the point of
resampling without replacement.
As far as the bootstrap is concerned, as far as I know
resampling MUST be carried out with replacement. This was
clearly stated at the outset of the literature (eg in
Efron-Tibshirani's 1993 book "with replacement" is in italics
the first time the resampling algorithm is described, at p. 45).
The rationale is that our aim is to generate artificial data
distributed as a multinomial given by the empirical distribution
function of the data. Note this holds for each artificial
datapoint.
What happens if use resampling without replacement? the various
artificial datapoints would be
generated with different multinomials. Further, we consider
this: if the bootstrap pseudodataset is of the same size of the
original dataset (as typical, although by no means necessary)
resampling with no replacement we end up with the original data!
bye,
Stefano
--
________________________________________________________________________
Stefano Fachin
Professore Ordinario di Statistica Economica
Dip. di Scienze Statistiche
"Sapienza" Università di Roma
P.le A. Moro 5 - 00185 Roma - Italia
Tel. +39-06-49910834
fax +39-06-49910072
web http://stefanofachin.site.uniroma1.it/